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-2x+1=6-\left(x-3\right)
Combine x and -3x to get -2x.
-2x+1=6-x-\left(-3\right)
To find the opposite of x-3, find the opposite of each term.
-2x+1=6-x+3
The opposite of -3 is 3.
-2x+1=9-x
Add 6 and 3 to get 9.
-2x+1+x=9
Add x to both sides.
-x+1=9
Combine -2x and x to get -x.
-x=9-1
Subtract 1 from both sides.
-x=8
Subtract 1 from 9 to get 8.
x=-8
Multiply both sides by -1.